GATE 2019 CS – Question 32
Two numbers are chosen independently and uniformly at random from the set $\{1,2,\dots,13\}$. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.49 to 0.51
Explanation
The numbers 1 to 7 have MSB 0 (7 numbers) and 8 to 13 have MSB 1 (6 numbers). The probability is $\frac{7^2+6^2}{13^2}=\frac{85}{169}=0.503$.